Question

A 90-kg mountain climber hangs from a nylon rope and stretches it by 25.0 cm. If the rope was originally 30.0 m long and its diameter is 1.0 cm, what is Young’s modulus for the nylon?

a) 4.32 × 10^9 N/m²
b) 6.45 × 10^9 N/m²
c) 8.21 × 10^9 N/m²
d) 9.78 × 10^9 N/m²

Answer 1

To find Young's modulus for the nylon rope, use the formula Y = (Force/Area)/(Change in length/Original length). Calculate the area of the rope using its diameter and the formula for the area of a circle. Substitute the values into the Young's modulus formula to find the answer.

Step-by-step explanation:

To find Young's modulus for the nylon, we can use the formula:
Y = (Force/Area)/(Change in length/Original length)

First, we need to calculate the area of the rope using its diameter. The radius would be half the diameter, which is 0.5 cm. We can then use the formula for the area of a circle, A = πr^2, to find the area of the rope.

Once we have the area, we can substitute the values into the Young's modulus formula to find the answer.